where we give \(H^0(L^{ik})^*\)  weight \(i\)  (not \(ik\) ). (Notice how this
cures the problem with Veronese embeddings described in Remark REF  above.)
This can also be shown to pull back the orbifold structure of weighted projective space to that of \(X\)  when \(L\)  is ample, and to pull \(\mathcal {O}(1)\)  back to \(L^k\) . However the corresponding Bergman kernel turns out not to be relevant to constant scalar curvature orbifold Kähler metrics. We learnt about the related alternative embedding (REF ) from Dan Abramovich; see [1]}. The idea of using weighted projective embeddings certainly goes back further to Miles Reid; see for instance [2]}.

